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Simplifying 18t2 + -3t + -5 = 0 Reorder the terms: -5 + -3t + 18t2 = 0 Solving -5 + -3t + 18t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.2777777778 + -0.1666666667t + t2 = 0 Move the constant term to the right: Add '0.2777777778' to each side of the equation. -0.2777777778 + -0.1666666667t + 0.2777777778 + t2 = 0 + 0.2777777778 Reorder the terms: -0.2777777778 + 0.2777777778 + -0.1666666667t + t2 = 0 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + -0.1666666667t + t2 = 0 + 0.2777777778 -0.1666666667t + t2 = 0 + 0.2777777778 Combine like terms: 0 + 0.2777777778 = 0.2777777778 -0.1666666667t + t2 = 0.2777777778 The t term is -0.1666666667t. Take half its coefficient (-0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. -0.1666666667t + 0.006944444447 + t2 = 0.2777777778 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667t + t2 = 0.2777777778 + 0.006944444447 Combine like terms: 0.2777777778 + 0.006944444447 = 0.284722222247 0.006944444447 + -0.1666666667t + t2 = 0.284722222247 Factor a perfect square on the left side: (t + -0.08333333335)(t + -0.08333333335) = 0.284722222247 Calculate the square root of the right side: 0.533593686 Break this problem into two subproblems by setting (t + -0.08333333335) equal to 0.533593686 and -0.533593686.Subproblem 1
t + -0.08333333335 = 0.533593686 Simplifying t + -0.08333333335 = 0.533593686 Reorder the terms: -0.08333333335 + t = 0.533593686 Solving -0.08333333335 + t = 0.533593686 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + t = 0.533593686 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + t = 0.533593686 + 0.08333333335 t = 0.533593686 + 0.08333333335 Combine like terms: 0.533593686 + 0.08333333335 = 0.61692701935 t = 0.61692701935 Simplifying t = 0.61692701935Subproblem 2
t + -0.08333333335 = -0.533593686 Simplifying t + -0.08333333335 = -0.533593686 Reorder the terms: -0.08333333335 + t = -0.533593686 Solving -0.08333333335 + t = -0.533593686 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + t = -0.533593686 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + t = -0.533593686 + 0.08333333335 t = -0.533593686 + 0.08333333335 Combine like terms: -0.533593686 + 0.08333333335 = -0.45026035265 t = -0.45026035265 Simplifying t = -0.45026035265Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.61692701935, -0.45026035265}
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